PRINCETON UNIVERSITY PRESS

Contents

Acknowledgments................................................................ix
Preface........................................................................xiii
Prologue From Myth to Reality..................................................1
One Einstein's Toolkit, and How to Use It......................................27
Two The Realm of the Nebulae...................................................52
Three Let's Do Cosmology!......................................................89
Four Discovering the Big Bang..................................................102
Five The Origin of Structure in the Universe...................................130
Six Dark Matter—or Fritz Zwicky's Greatest Invention.....................174
Seven Dark Energy—or Einstein's Greatest Blunder.........................202
Eight The Modern Paradigm and the Limits of Our Knowledge......................229
Nine The Frontier: Major Mysteries That Remain.................................253
Appendixes.....................................................................263
Glossary.......................................................................281
Bibliography...................................................................291
Index..........................................................................295

Chapter One

Einstein's Toolkit, and How to Use It

 Overconfidence among the Cognoscenti
at the Dawn of the Twentieth Century

As the nineteenth century drew to a close and the new century
dawned, an intellectual ferment spread across the disciplines comprising
western culture. Art, music, literature, and science were
radically transformed in the Modernist period to a degree comparable
to the changes that occurred in the Renaissance and the Enlightenment.
The revolutionary expansion of our cosmic consciousness,
which we will detail in the next chapter, was paralleled
by the revolution in our scientific tools—the laws of physics. But at
first no one saw the changes that were coming in both physics and
astronomy. The complacent, turn-of-the-century belief that the
laws of physics were essentially nailed down, with only refinements
to follow, was blown apart by Albert Einstein, who single-handedly
initiated the revolutions of quantum mechanics, special
relativity, and general relativity. In the next twenty years, he and
his colleagues established the new physics that provided the foundations
for our modern cosmology.

Let's begin our exploration of the physics revolution in 1894.
Professors have gathered for a lecture in a new, neo-gothic building,
a curious amalgam of the ancient and the modern at the just
established University of Chicago. In his ceremonial, opening address,
Albert Michelson, the director of the laboratory, said:

The more important fundamental laws and facts of physical
science have all been discovered, and these are now so firmly
established that the possibility of their ever being supplanted
in consequence of new discoveries is exceedingly remote. Future
discoveries must be looked for in the sixth place of
decimals.

How wrong he was. Michelson himself went on to become the
most accomplished optical experimentalist of his age and to perform
the Michelson-Morley experiment that helped to confirm
Einstein's revolutionary new physics. Simon Newcomb, head of
the United States Nautical Almanac Office, had dismissed the possibility
of future astronomical discoveries somewhat earlier, in
1888, but then later gave us the best measurement of the speed of
light.

Even today, books proclaiming the end of scientific discovery
are published. As recently as 1996 one of us was asked on a popular
television program to comment on a new book, The End of
Science, which maintained that we had come to the end of discovery
and in fact were at the end of the investigation of the big questions.
It was fairly easy to make the case that we still did not know
the answers to the really big questions that any child might ask:
How did the world begin? How will it end? What is the world
made of? Are we alone in the universe? Clearly, big questions remain
to be answered.

But in the late nineteenth century, because Newton's laws of
motion and gravitation seemed to have successfully explained dynamical
phenomena in the heavens and on the Earth, it really did
appear to many physicists and to astronomers that the operation of
physical laws was clear and that our knowledge of the universe was
essentially complete. The subject of astronomy was primarily understood
to be measuring the positions of the planets on the sky,
computing their expected positions, and comparing the two approaches
with honesty and care. True, the calculations could be
tediously complex; but everything could be accounted for in principle,
even if the applied mathematicians still had to work out the
details to six or more decimal places.

Everything also appeared to be satisfactory with the laws of electricity
and magnetism. A bushy-bearded Scotsman, James Clerk
Maxwell, had brilliantly unified electricity and magnetism in 1861
with the introduction of Maxwell's equations, thereby providing a
new synthesis of existing physical laws. The science of thermodynamics,
so useful in the industrial revolution for understanding
heat, temperature, and steam engines, could likewise be considered
mature, with little potential for further development. It
seemed to some that physics was being killed off by its own success;
instead of pursuing natural philosophy, the physicists would
have to occupy themselves doing applied science.

Scientists had no way of knowing that their physics and astronomy
was, in fact, hugely incomplete and that great breakthroughs
awaited them. To the extent that scientists at the time were aware
of not having the full picture, the knowledge gaps seemed slight.
For example, in astronomy there was a slight worry over the motion
of the planet Mercury, the elliptical orbit of which rotated
with respect to the Sun at a slightly faster rate than predicted by
Newton's laws. But this "advance of the perihelion of Mercury" appeared
to many as a small detail that the mathematicians would
surely resolve, given more time. Looking further out, many felt
that the mysterious spiral nebulae—milky patches in the heavens
that piqued the interest of natural philosophers and astronomers
from Immanuel Kant to William Herschel—were planetary systems
in the making. The idea proposed by Kant and others that
they were "island universes" comparable to our own Milky Way
galaxy had been dropped, as had William Herschel's claim that
nebulae were star clusters. In 1885, the astronomer and writer
Agnes Mary Clerke had this to say on the structure of nebulae:

The question whether the nebulae are external galaxies
hardly any longer needs discussion. It has been answered by
the progress of discovery. No competent thinker, with the
whole of the available evidence before him, can now, it is safe
to say, maintain any single nebula to be a star system of coordinate
rank with the Milky Way. A practical certainty has
been attained that the entire contents, stellar and nebular, of
the sphere belong to one mighty aggregation.

As the nineteenth century passed into history, the conviction was
widespread that the entire universe consisted of just one island, the
Milky Way, and that we, on planet Earth revolving around the Sun,
were centrally located in that galactic system. The facts of astronomy
and the laws of physics were completely determined.

* Revolution in Physics: The Inception
of Quantum Theory and Relativity

The startling new discoveries that transformed the dominant, but
incomplete world-view of the new century did not emerge from a
laboratory or even a telescope; rather, they were the result of pure
thought. Einstein detected two glaring inconsistencies of logic
within the scientific canon. First, he realized that two sets of experiments
analyzing the paths taken by ordinary light were apparently
inconsistent with one another. And second, he realized that
Maxwell's equations, which explained all experimental data in the
fields of electricity and magnetism, were actually inconsistent with
Newton's laws.

In the first breakthrough, he realized that some accepted experiments
were inconsistent with the wave nature of light that
was fundamental to Maxwell's equations—and this led him to
postulate a particle aspect to light rays, a development that immediately
pushed physics toward the quantum interpretation of
microscopic phenomena and which ultimately upended all of
classical physics.

This all happened in 1905, Einstein's annus mirabilis, during a
four-month frenzy of research activity while he was still employed
as a clerk in the Swiss patent office in Bern. Here, in translation, is
his summary of the breakthroughs, extracted from a letter he
wrote in May 19o5 to his friend Conrad Habicht:

Why have you still not sent me your dissertation ... you
wretched man? I promise you four papers in return. The first
deals with radiation and the energy properties of light and is
very revolutionary ... The second paper is a determination
of the true sizes of atoms ... The third proves that bodies on
the order of magnitude 1/1000 mm, suspended in liquid,
must already perform a random motion that is produced by
thermal motion. The fourth paper is only a draft at this point,
and is on electrodynamics of moving bodies that employs a
modification of the theory of space and time.

The first paper, which is, according to some scholars, the most
revolutionary in the history of physics, contains Einstein's suggestion
that light comes not just in waves but in tiny packets of energy,
quanta of light, later called photons. At this moment in history,
Max Planck had already hinted that energy is "composed of a very
definite number of equal finite packages" as he stated in December
19oo at the Berlin Physical Society. But well-established diffraction
experiments—in which a beam of light, passing through two slits
in an opaque wall, can be seen to interfere with itself—had demonstrated
the wave nature of light.

At the heart of Einstein's first 1905 paper was the central question
bedeviling physics: is the universe made of particles, or is it
the unbroken continuum of electromagnetic and gravitational
fields described by classical physics? Einstein effectively argued
that light could be both. That is, the particulate nature of light is an
intrinsic property of light itself rather than a description of how
light interacts with matter. Henceforth physicists would adopt this
duality: light could behave as either a continuous wave motion
(classical physics) or as a stream of quanta (quantum physics).
Einstein's work made necessary the developments, which are still
not complete, that could unify the classical and quantum modes of
describing nature. Other physicists, including Paul Dirac, did succeed
in the next decades, uniting quantum mechanics with electricity
and magnetism. However, a quantum theory of gravity continues
to elude our grasp.

Einstein's second and third papers provided evidence, from already
accepted experiments, for the reality of atoms and molecules.
The theoretical physicist Max Born recalled in 1949, "At the
time atoms and molecules were still far from being regarded as
real." The three papers thoroughly demonstrated the exceptional
creativity of young Einstein; but, important as these works of 1905
were, our interest lies primarily in Einstein's fourth paper on special
relativity, which startled the world by proposing new properties
for space and time, thereby introducing revolutionary new
ideas about the nature of the universe to the world and forever altering
our concepts of physical reality. The invention of special
relativity successfully effected the merger of Newton's dynamics
with electricity and magnetism.

But none of this touched on gravity, a central component of
Newton's laws and at the heart of all cosmic investigations. Einstein
realized the defect and remedied it a decade later with general
relativity, providing, at last, the update for Newton that was
consistent with all known macroscopic experiments and also
consistent in its formulation with Maxwell's laws. However, as we
noted, the final union of a gravity and quantum mechanics has not
yet been achieved, even to the present day, and it remains the holy
grail of string theory and its rivals.

It is worth spending a little more time in these early years, since
the stage was set then, philosophically, for all the subsequent reformulations
of our concepts of space, time, and causality.

* Special Relativity

Two aspects of classical physics deeply impressed Einstein. First,
there was Newton's comprehensible clockwork universe in which
causes produced effects, forces acted on objects, and in theory everything
could be predicted from initial conditions by the mathematical
rules governing gravity, mass, force, and motion. Einstein
liked this strict causality: "the profoundest characteristic of Newton's
teaching," as he put it.

The second great pillar of classical physics to impress young
Einstein was electromagnetism, the field in which Michael Faraday
and lames Clerk Maxwell blazed the trail. In the mid-nineteenth
century, Newton's mechanics was joined by Faraday's
work on electricity and magnetism (the latter pioneered by America's
first great scientist, Benjamin Franklin, in the mid-eighteenth
century). Faraday showed that an electric current produces magnetism,
and a changing magnetic field can induce a current in a
conducting wire. Maxwell's equations united electrical and magnetic
phenomena by showing that the coupling between the two is
achieved by an electromagnetic wave.

At an experimental level the equations of Newton's mechanics
and Maxwell's electromagnetism were known to be correct to a
high degree of precision. But Einstein realized that, at a deeper
level, they were actually in conflict. They were logically inconsistent
with one another. Over time, Einstein came to a profound
conclusion—that either Newton or Maxwell (or both of them for
that matter) must be wrong somewhere; and eventually he resolved
the conflict by thought experiments.

In the hope of finding what was wrong, Einstein considered
how the experiments of two observers at motion with respect to
one another must differ. First, he supposed that in one frame of
reference an investigator finds that both Maxwell's and Newton's
theories are exactly correct to an infinite degree of precision. He
was then able to show that for the second, equally qualified observer,
moving at some constant velocity with respect to the first
observer, both theories would not be true. The experiments of the
second observer would show that both theories could not be true:
one or both were false. This followed from the intrinsic mathematical
framework of the two theories and led to an impossible situation:
the two theories might be correct for one observer, but then
one or the other would be incorrect for another who is moving at
a constant velocity with respect to the first one.

Which is the "right" observer? Einstein realized Newton's and
Maxwell's theories were logically inconsistent, and he suspected
that it was Newton's theory that was false. No physical experiments
were performed and none were needed. In fact, the predicted failures
would have been so small as to be undetectable given the experimental
techniques of the time. This logical inconsistency between
the two sets of accepted laws led him to invent special
relativity as a first attempt to fix the Newtonian paradigm.

Unlike the majority of theoretical physicists, Einstein's working
methods did not involve covering dozens of pages a day with
trial-and-error equations. Rebellious of authority and skeptical of
anything that could not be observed, he said of himself that he
preferred "to think in pictures." Further thought experiments convinced
him that the conflict between Newton's laws of mechanics
and Maxwell's equations concerned the speed of light. Why, he
wondered, did Maxwell's field equations include the velocity of
light when Newton's did not?

He began with two postulates, the first of which is the principle
of relativity: the fundamental laws of physics must be the same for
all observers moving at a constant velocity with respect to each
other. This is based on the intuition of Galileo and is called "Galilean
Relativity." There is no experiment do that will tell you your
absolute velocity, although observations can measure velocity with
respect to some other observer: an experimentalist below decks in
a smoothly traveling ship could never determine the ship's speed.
Einstein's second postulate was that the speed of light through
empty space is independent of the state of motion of the emitting
body. At first Einstein had great difficulty in reconciling these two
postulates with his thought experiments, which involved moving
trains (a tradition that lives on in today's textbooks). His frequent
visits to the huge Zurich train station with its synchronized clocks
provided the setting. The solution really did come in a flash, and
we'll use Einstein's thought experiment to explain it.

An observer is standing on the embankment of a railway track
exactly halfway between two distant towns, A and B. This stationary
observer sees two bolts of lightning simultaneously strike
church steeples in towns A and B. At the same moment, there is a
train on the tracks midway between A and B, and an observer inside
the train is at the midway point. The train is traveling from A
to B. The train observer is therefore moving toward B and away
from A. While the light from B is rushing toward the observer on
the train, the motion of the train will take the observer closer to
the onrushing light signal from B and farther away from the light
signal from A. The train observer therefore sees the flash from B
before the flash from A.

This leads to a conclusion that would become immensely important
in observational cosmology. Events that are simultaneous
at one point of reference are not simultaneous for a moving observer
at exactly the same spatial location. This may seem trivial,
but it is not. It means that there is no absolute time. Time does not
go tick-tock all over the universe independent of the observer's
frame of reference. This shattered a premise that Newton had
made in Principia more than two centuries earlier.

The equations of motion now became a little more complicated
than the Newtonian versions. In order to write equations that
would work perfectly in frames of reference that are moving at
constant velocity with respect to each other, Einstein had to attach
a fourth dimension, time, to the three spatial dimensions. That deft
move altered the representation of geometry in the universe from
three-dimensional graph paper to a four-dimensional space-time
continuum. The future implications for cosmology were immense
because, as we shall see, modern cosmology involves the interpretation
of observations from parts of the universe that are both remote
in time and are moving at enormous velocities relative to our
vantage point in the Milky Way.

There is a fifth paper from the 1905 annus mirabilis. September
finds Einstein penning another letter to Habicht in which he casually
remarks that mass is a direct measure of the energy contained
in a body, and he states that light carries mass with it. His paper,
published in the journal Annalen der Physik, fills just three pages,
but contains the most famous equation in physics, E = mc2, imprinted
on thousands of T-shirts to this day. This formula means
that the energy, E, equivalent to a body of mass, m, can be found by
multiplying it by c2, the square of the speed of light. Because the
velocity of light is so great, very small changes in the mass of an
object can release or absorb enormous amounts of energy. The
truth of this equation would be realized in atomic weapons, nuclear
power, and as we will see, the shining of the Sun and most
stars. It provided the essential clue to those scientists, half a century
later, who tried and succeeded in solving the ancient problem
of how the Sun continues to shine, of how it has sufficient fuel to
continue, when all conventional sources of energy would have
been exhausted long ago.